Communications Minister Malcolm Turnbull has denounced the ''vicious ingratitude'' of the artists who forced the withdrawal of Transfield as a sponsor of the Biennale arts festival over the company's involvement in offshore processing of asylum seekers.

Mr Turnbull said losing the company, the festival's founding sponsor, could spell the end of the event.

"Really, this is disastrous," Mr Turnbull said. "If we lose the Biennale as a consequence of this that would be an absolute tragedy."

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The artists had threatened to boycott the Biennale of Sydney because it accepted money from founding partner Transfield Holdings, a company with a 12 per cent shareholding in Transfield Services, which won a $1.2 billion contract to run the Abbott government's immigration detention centres on Nauru and Manus Island.

But while the artists have claimed victory in forcing Transfield Holdings to sever its 40-year tie with the arts festival, they may have achieved the opposite of their objective, the Communications Minister said.

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Instead of encouraging the Abbott government to reconsider its harsh asylum seeker policies, the artists had succeeded in sidelining one of Australia's great philanthropic families, who had generously supported the arts for more than 50 years, Mr Turnbull said.

"I hope the Biennale can survive but I think the artists that have done this have potentially driven a stake, not through the asylum seeker policy, I can assure you of that, but through the heart of the Biennale itself," Mr Turnbull told ABC radio on Monday.

"There wouldn't be a Biennale without the Belgiorno-Nettis family," he added. "Franco, Luca's father, was one of the great patrons of the arts, a sort of latter day Medici.

"I think it's an extraordinary ... the sheer vicious ingratitude of it all."

He said that if the artists had a problem with the Abbott government's asylum seeker policies they should boycott any arts events that accepted any funding from the federal government.

"Transfield doesn't make government policy," he added. "It's in business. It is fulfilling a contract for the government".

Luca Belgiorno-Nettis tendered his resignation as chair of the Biennale board last Friday, which the Biennale board "reluctantly" accepted and ended its partnership with Transfield Holdings.

"We have listened to the artists," the Biennale board wrote in its statement.

Mr Belgiorno-Nettis said the protests had reached a "crescendo" and he resigned so that "some blue sky may open up over this 19th Biennale of Sydney".

"Biennale staff have been personally vilified with taunts of 'blood on your hands'," Mr Belgiorno-Nettis said.

"I have been personally vilified with insults, which I regard as naïve and offensive.

"This situation is entirely unfair – especially when directed towards our dedicated Biennale team who give so much of themselves."

Mr Turnbull said he hoped Mr Belgiorno-Nettis and the Biennale board would reconsider their decisions.

Arts Minister George Brandis told Fairfax Media that Transfield was "a good corporate citizen" and he welcomed their "generosity and support for a variety of arts companies and institutions".

But the protesting artists have indicated they will continue to target Transfield and arts organisations that receive its sponsorship dollars.

Artist Gabrielle de Vietri, who led the Transfield campaign, said other companies profiting from the policy of offshore detention centres would also be scrutinised.

"We are going to pursue this through divestment workshops and seeing how much more we can affect this policy through targeting the companies that are profiting from mandatory detention," she said.

The Transfield Foundation also supports the Australian Chamber Orchestra and Accessible Arts NSW.

De Vietri said the Museum of Contemporary Art Australia and the AGNSW were among institutions that could suffer a backlash from artists over Transfield links.